What is the geometric representation of the equation x + 2y = 4?

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Question: What is the geometric representation of the equation x + 2y = 4?

Options:

Correct Answer: A line

Solution:

The equation x + 2y = 4 represents a straight line in a two-dimensional space.

What is the geometric representation of the equation x + 2y = 4?

What is the geometric representation of the equation x + 2y = 4?

Step 1: Understand that the equation x + 2y = 4 is in the form of a linear equation.
Step 2: Recognize that linear equations represent straight lines when graphed on a coordinate plane.
Step 3: Identify the variables: x is the horizontal axis (x-axis) and y is the vertical axis (y-axis).
Step 4: Rearrange the equation to the slope-intercept form (y = mx + b) to find the slope and y-intercept.
Step 5: Solve for y: 2y = 4 - x, then y = (4 - x)/2, which simplifies to y = -0.5x + 2.
Step 6: Identify the slope (m = -0.5) and the y-intercept (b = 2).
Step 7: Plot the y-intercept (0, 2) on the graph.
Step 8: Use the slope to find another point: from (0, 2), go down 0.5 and right 1 to get to (1, 1.5).
Step 9: Draw a straight line through the points (0, 2) and (1, 1.5).
Step 10: Conclude that the line represents all the solutions to the equation x + 2y = 4.

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